SOLUTION: A ladder AB, which is set up with B on a horizontal ground and vertical wall, makes an angle of 71 degree with the ground. It is prevented from slipping by a tight rope PQ of lengt

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Question 1132210: A ladder AB, which is set up with B on a horizontal ground and vertical wall, makes an angle of 71 degree with the ground. It is prevented from slipping by a tight rope PQ of length 1.6meters, fixed at P to the foot of the wall and at Q to the ladder, PQ being at the right angles to AB. Calculate in centimetres, the height AP of the ladder above P and length of the ladder.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A ladder AB, which is set up with B on a horizontal ground and vertical wall, makes an angle of 71 degree with the ground.
It is prevented from slipping by a tight rope PQ of length 1.6meters, fixed at P to the foot of the wall and at Q to the ladder, PQ being at the right angles to AB.
Calculate in centimetres, the height AP of the ladder above P and length of the ladder.
:
Draw a diagram of this as described.
:
Change 1.6 m to 1600 cm
A right triangle is formed ABP
Find the angle at A: 180 - 90 - 71 = 19 degrees
:
Another right triangle is formed by the rope. QBP
Find the distance (d,the hypotenuse) from the base of the ladder to the base of the wall(BP)
sin(71) = 1600%2Fd
d = 1600%2Fsin%2871%29
d = 1692 cm from the base of the ladder to the wall.
:
Find the length (L) (the hypotenuse) of the ladder using the sine of 19 degrees
sin(19) = 1692%2FL
L = 1692%2Fsin%2819%29
L = 5197 cm is the length of the ladder, AB
Find the height (h) using the tangent of 19 degrees
tan(19) = 1692%2Fh
h = 1692%2Ftan%2819%29
h = 4914 cm is height to point on the wall, AP